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[50] L Kosten Stochastic theory of data-handling systems with groups of multiple sources In H Rudin and W Bux, eds, Performance of Computer-Communication Systems, pp 321 331 Elsevier, New York, 1984 [51] P Lassila and J Virtamo Ef cient importance sampling for Monte Carlo simulation of loss systems In 16th International Teletraf c Congress ITC16, Edinburgh, 1999 [52] P Lassila and J Virtamo Nearly optimal importance sampling for Monte Carlo simulation of loss systems ACM Transactions on Modeling and Computer Simulation, 10: 326 347, 2000 [53] N Likhanov and R Mazumdar Cell loss asymptotics in buffers fed with a large number of independent stationary sources Journal of Applied Probability, 36: 86 96, 1999 [54] M Mandjes Rare event analysis of batch-arrival queues Telecommunication Systems, 6: 161 180 [55] M Mandjes Asymptotically optimal importance sampling for tandem queues with Markov uid input AEU International Journal on Electronics and Communications , 52: 152 161, 1998 [56] M Mandjes Fast simulation of blocking probabilities in loss networks European Journal of Operational Research, 101: 393 405, 1998 [57] M Mandjes and A Ridder Finding the conjugate of Markov uid processes Probability in the Engineering and Informational Sciences, 9: 297 315, 1995 [58] M Mandjes and M van Uitert Sample-path large deviations for tandem and priority queues with Gaussian inputs Annals of Applied Probability, 15: 1193 1226, 2005 [59] M Mandjes and B Zwart Large deviations for sojourn times in processor sharing queues Queueing Systems, 52: 237 250, 2006 [60] Z Michna On tail probabilities and rst passage times for fractional Brownian motion Mathematical Methods of Operations Research, 49: 335 354, 1999 [61] D Miretskiy, W Scheinhardt, and M Mandjes Ef cient simulation of a tandem queue with server slow-down Simulation, 83: 751 767, 2007 [62] I Norros, P Mannersalo, and J L Wang Simulation of fractional Brownian motion with conditionalized random midpoint displacement Advances in Performance Analysis, 2: 77 101, 1999 [63] S Parekh and J Walrand Quick simulation of rare events in networks IEEE Transactions on Automatic Control, 34: 54 66 [64] V Paxson Fast, approximate synthesis of fractional Gaussian noise for generating self-similar network traf c Computer Communication Review , 27: 5 18, 1997 [65] K Ramanan and P Dupuis Large deviation properties of data streams that share a buffer Annals of Applied Probability, 8: 1070 1129, 1998 [66] L Rojas-Nandayapa and S Asmussen Ef cient simulation of nite horizon problems in queueing and insurance risk Queueing Systems, 57: 85 97, 2007 [67] J Sadowsky On Monte Carlo estimation of large deviations probabilities Annals of Applied Probability, 6: 399 422, 1996 [68] J Sadowsky and J Bucklew On large deviations theory and asymptotically ef cient Monte Carlo estimation IEEE Transactions on Information Theory, 36: 579 588, 1990
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[69] A Shwartz and A Weiss Large Deviations for Performance Analysis Queues, Communications, and Computing Chapman & Hall, London, 1995 [70] D Siegmund Importance sampling in the Monte Carlo study of sequential tests Annals of Statistics, 4: 673 684, 1976 [71] Wikipedia http://enwikipediaorg/wiki/Normal distribution, 2008 [72] W Willinger, M Taqqu, R Sherman, and D Wilson Self-similarity through high-variability: statistical analysis of Ethernet LAN traf c at the source level IEEE/ACM Transactions on Networking, 5: 71 86, 1997 [73] D Wischik Sample path large deviations for queues with many inputs Annals of Applied Probability, 11: 379 404, 2001
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This chapter deals with dependability models originating, for instance, in computer science or networking systems The basic modeling assumption is to consider a multicomponent system (ie, a multidimensional model) such that each component is subject to failure and possibly to repair The global system is then considered to be down (typically a rare event in most applications of interest) when it is in some subset of states such that given components are themselves down The principal dependability measures we are interested in are the mean time to failure (MTTF), representing the average time to reach the set of failed states starting from a given point; the unavailability at a given time t, that is, the probability that at time t the model is in one of its failed states; the steady-state unavailability; and the unreliability at time t, which is the probability that the model enters the subset of failed states at or before t These are not the only dependability measures of interest There are many others, such as the interval availability at t, a random variable de ned as the fraction of [0, t] during which the system is in an operational state In the chapter, we will discuss only methods designed to evaluate the main metrics in the area
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Rare Event Simulation using Monte Carlo Methods Edited by Gerardo Rubino and Bruno Tuffin 2009 John Wiley & Sons, Ltd ISBN: 978-0-470-77269-0
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